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Power Engineering Briefing Note Series

pebn rv1.2.doc Page 3 24-Jul-08

BH Curve and Iron Loss Measurements

for Magnetic Materials

PEBN #5 (12 May 2008)

W.L. Soong

School of Electrical and Electronic Engineering

University of Adelaide, Australia

soong@ieee.org Abstract - This brief discusses the measurement of the BH curve and iron loss characteristics of magnetic materials based on tests on cores done at mains frequency.

I. INTRODUCTION

The BH loop of a magnetic material represents the

relationship between its magnetic flux density B as a function of the magnetic field intensity H. For an ideal lossless, linear magnetic material the curve would be a straight line whose slope is equal to the permeability of the material (see Fig.

1a). Practical effects include : magnetic saturation that limits

the maximum achievable magnetic flux density in the material and so causes the BH curve to be non-linear (see Fig. 1b), and iron losses which cause the BH curve to become a loop whose area represents the energy losses due to effects such eddy- current and hysteresis loss (see Fig. 1c). B H a) ideal BH loop b) with saturation c) with saturation and low iron loss Fig. 1. The effect of saturation and iron loss on the shape of the BH loop.

II. BH LOOP MEASUREMENT PRINCIPLES

The magnetic properties and in particular the iron losses are sensitive to mechanical stress and the heat treatment used in the laminations. Standard BH curve and iron loss measurements are normally made using a square-shaped stack of laminations called an Epstein frame [1]. It is however possible to make measurements using other core shapes. It is important that the core have a uniform cross-sectional area otherwise it is difficult to interpret the results because B and H are not uniform in the material. In Fig. 2 the core has a circular shape. i main AC N main v

Fig. 2. Test arrangement for measuring BH loops.

The magnetic core has two windings. The main winding is used to create the magnetic field intensity H. The magnetic field intensity is given by : main main core

Ni tHtl (1)

where Nmain is the number of turns in the main winding, i main is the current flowing in the main winding and l core is the mean magnetic path length of core (shown as a dashed line in Fig.

2). In order to create high levels of magnetic field intensity to

saturate the material (e.g. 10 kA/m) it is necessary that the main winding has many turns of relatively thick wire which can carry high levels of current.

The required rms AC supply voltage V

s for the main winding is given by : 4.44 smain pk core

VNBAf (2)

where B pk is the expected saturation flux density of the core, A core is the magnetic cross-sectional area of the core (see Fig.

2) and f is the supply frequency.

The sense coil winding is used to measure the magnetic flux density B created by the main winding current. The induced voltage in the sense coil winding v sense is given by : sense sense sense core dt dBtvtN NAdt dt (3) where N sense is the number of turns in the sense winding. Re- arranging (3) to solve for the flux density produces : sense sense core sense core sense

Bt v dt tAN AN

(4) where sense is the instantaneous flux-linkage of the sense coil which is the integral of the sense coil voltage. This integration can be approximated for a sampled waveform by : @>@1 sense sense sense kkvkt ' (5) where t is the sampling time interval and k represents the sample number. Unlike what is shown in Fig. 2, both the main and sense coil windings are uniformly distributed around the magnetic core to produce a more uniform magnetic field distribution in the core and also to improve the magnetic coupling between the two windings. P loss in the core is given by : T mainloss sense main sense

NPvidtNT

(6) where T is the period of the supply waveform. This expression can be approximated for sampled data as : 1 1

Kmainloss sense main

sense k

NPvkikNK

(7) where K is the number of samples in one period.

Power Engineering Briefing Note Series

pebn rv1.2.doc Page 4 24-Jul-08 -2-1012

Main Coil Current [A]

-2-1012

Sense Coil Voltage [V]

Imain

Vsense

Fig. 4. Examples of measured main coil current and sense coil voltage. -1.5-1.0-0.50.00.51.01.5 -1500 -1000 -500 0 500 1000 1500

Field Strength (A/m)

Flux Density (Tesla)

Fig. 5. Example of measured BH loop corresponding to data in Fig. 4. -1.5-1.0-0.50.00.51.01.5 -1500 -1000 -500 0 500 1000 1500

Field Strength (A/m)

Flux Density (Tesla)

Fig. 6. Example of BH loops for other values of peak flux density. When the core is heavily saturated, the low power-factor of the waveforms means that the power loss calculation is very sensitive to small phase shift differences between the voltage and current sensors. These errors can cause the power loss calculation result to become negative at high currents. An alternative and possibly more accurate power loss measurement method is to also feed v sense and i main signals to a power analyser and to record the power reading from this. III.

TEST AND ANALYSIS PROCEDURE

A.

Test Method

The test arrangement was shown in Fig. 2. The main winding is connected to a variable-magnitude, low-voltage AC source which can be safely produced from the output of a step- down transformer connected to an auto-transformer.

The main winding current i

main (t) and the sense winding voltage i sense (t) are measured using appropriate sensors and are sampled at a rate to give say 200 to 1000 samples per cycle and to record an integral number of cycles, say two. Sets of voltage and current measurement are taken from zero to the maximum peak flux density value in say six to ten steps. A reading proportional to the peak flux density magnitude can be obtained by connecting a standard AC voltmeter (not "true RMS") to the sense coil winding. This

0.00.20.40.60.81.01.21.41.61.82.0

0 2000 4000 6000 8000 10000 12000

Field Strength (A/m)

Flux Density (T)

Fig. 7. Measured BH characteristics based on the peak values of B and H measured for each data set.

024681012

0.0 0.5 1.0 1.5 2.0

Peak Flux Density (T)

Iron Loss (W/kg)

Fig. 8. Measured iron loss characteristics.

reading can be used to set the supply voltage to obtain sets of data at roughly equal steps in peak flux density. For each voltage and current data set, the following procedure can be used for analysis : remove any DC offsets in the measured voltagequotesdbs_dbs7.pdfusesText_5

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